1. Last Time: Introduction to Gravity Governed by LaPlace’s equation: with solution of the form: If we have a spherical body with mass M and constant (or radially symmetric) density, this integral becomes: Method looks for anomalies in gravity  g (relative to the gravity expected for a uniform-density ellipsoid) that result from lateral changes in mass density  Measurements may be surface-based or space-based ; absolute or relative Geology 5660/6660 Applied Geophysics © A.R. Lowry 2016 For Wed 16 Mar: Burger 349-378 (§6.1-6.4) 14 Mar 2016

2. Example: (Image from GFZ-Potsdam) Global free-air gravity from satellite & ground measurements

3. Gravity Measurements: I. Absolute Gravity : Measure the total field  time of a falling body prism vacuum laser ~2m Must measure time to ~10 -11 s; distance to ~10 -9 m for 1  gal accuracy! Nevertheless this is the most accurate ground-based technique (to ~3  gal) Disadvantages: unwieldy; requires a long occupation time to measure

4. Gravity Measurements: II. Relative Gravity : Measures difference in at two locations. Pendulum : difference in period T : Errors in timing of period T  ~0.1 mgal Mass on a spring : M  g = k  l or  g = k  l / M Worden and Lacoste-Romberg are of this type (“zero-length” spring of L-R yields errors around 6  gal) l mass M length l spring constant k

5. Gravity Measurements: III. Satellite Gravity : Measure (from space) the height of an equipotential surface (called the geoid, N ) relative to a reference ellipsoid.

6. Gravity Measurements: Ocean Altimetry : Measure height of the ocean surface using radar or laser (e.g., SEASAT, JASON) Satellite Ranging : Satellite orbits follow the geoid Measure orbits by ranging from the ground to the satellite or ranging between two satellites (e.g., GRACE) N III. Satellite Gravity : Measure (from space) the height of an equipotential surface (called the geoid, N ) relative to a reference ellipsoid

7. Example: (Image from GFZ-Potsdam) Global free-air gravity from satellite & ground measurements

8. GRACE designed for time-variable gravity, mostly hydrosphere

9. GRACE Mass Trend 2003-2010: (Jacob et al., Nature, 2012) Total mass trendCorrected for solid Earth (i.e., hydrology + cryosphere)

10. Image from UT-CSR/NASA GRACE-derived mass trend over Greenland shows melting and accumulation; net loss is 222±9 km 3 /yr! Contributions to global sea level change: Greenland: 0.61±0.02 mm/yr Antarctica: 0.45±0.20 mm/yr Continental: 0.41± 0.08 mm/yr Ice total: 1.48 Altimetry: 3.3

11. CARI (GPS) But GRACE gives solid Earth info too!

12. Example: Free Air Gravity from Satellite Ocean Altimetry

13. (Note altimeters were actually intended to find out more about sea level change!)

14. Detail: Indian Ocean (East of Madagascar)

15. Detail: Western Pacific